A computationally efficient identification procedure is proposed for a non-Gaussian white-noise-driven linear, time-invariant, nonminimum-phase system. The method is based on the idea of computing the complex cepstrum of higher-order cumulants of the system output. In particular, the differential cepstrum parameters of the nonminimum-phase impulse response are estimated directly from higher-order cumulants by least-squares solution or two-dimensional FFT operations. The method reconstructs the minimum-phase and maximum-phase impulse response components separately. It is flexible enough to be applied on autoregessive (AR), moving average (MA), or ARMA systems without a priori knowledge of the type of the system. Benchmark simulation examples demonstrate the effectiveness of the method even with short length data records.